Bone local coordinate adjustment
To align bones in Edit Mode select the bone you want to align and then the bone you want to copy the alignment from. Then press Ctrl Alt A (Align Bones).

As a side note: If you need them to have different rotations, parent them on additional bones and use the copy location constraint on the parents instead. That way you can rotate the childs freely without worrying about their translation.

An easier solution might be to use Pose Space to Pose Space for the copy location constraint and tick on Offset in the constraints panel.